Origin of stick-slip motion in a driven two-wave potential

A model is presented of a particle that interacts with two periodic potentials, representing two confining plates, one of which is externally driven. The model leads to a spectrum of rich behaviors in the motion of the top driven plate: a stick-slip, intermittent kinetic regime, characterized by force fluctuations, and two types of sliding above a critical driving velocity v(c). Similar behaviors are typical of a broad range of systems including thin sheared Liquids. A detailed analysis of the different regimes displays an interesting transition range between stick-slip and kinetic motion, omega(-2) power spectra of the force over a wide range of velocities below v(c), and a decrease of the force fluctuations that follows (v(c)-v)(1/2) for v<v(c). The velocity-dependent Liapunov exponents demonstrate that stick-slip dynamics is characterized by chaotic behavior of the top plate and the embedded particle. An equation is derived that provides a coarse-grained description of the plate motion near v(c).